Mr Cole-Hamilton took the reins of his party on Friday, succeeding Willie Rennie, less than an hour after a deal between the SNP and Scottish Greens was unveiled.
The deal will see the Greens support the majority of Government legislation, while also having two MSPs take ministerial office – although both sides say the agreement is not a formal coalition.
Mr Cole-Hamilton’s party is the most recent example of the perils of coalition working, after the Lib Dems were decimated at the ballot box in recent general elections following their partnership with the Conservatives at Westminster in 2010.
Speaking on BBC Radio Scotland’s Good Morning Scotland programme on Saturday morning, the new Lib Dem leader was scornful of the newly announced SNP-Green pact.
Mr Cole-Hamilton said: “This is just formalising a relationship that has existed in Scotland for years.
“I think it looks like pretty thin gruel for the Green Party, they’ll soon realise that they will have to carry the can for all of the SNP’s inadequacies on public policy.
“Whether that’s the threadbare state of our police force, the waiting times – that people are clutching letters that say they will be seen in 12 weeks when there isn’t a chance they’ll be seen in 50.
“This is all part of the Greens’ deal, they’re going to have to carry the can for all this and, you know, good luck to them.”
The new leader also made an attempt to distance himself from the 2010 coalition, saying: “I wouldn’t really be able to advise the Greens on coalition, because I was never part of that, I wasn’t in elected politics when that happened.
“I’m the first post-coalition generation Liberal Democrat who has sought and won the leadership of the party in Scotland.
“I understand the damage that the coalition did to my party, we’ve had to work hard to regain trust and belief and there were decisions that were taken in that time I would have pushed back on.
“This is a new generation of Lib Dem talent that’s coming to the fore, not just with me but with a raft of crackling new candidates who are brimming with talent and a new hope coming to the fore.”
Mr Cole-Hamilton said in the lead up to his anointment as leader, after no other candidates came forward, he would work with the Tories to save the union.
But he said he currently considers the Conservatives to be “part of the problem”.
He said: “I will make the positive case for the union with anybody, but it has to be a reformed union.
“At the moment, the Conservatives are part of the problem. We are trapped between a clash of two nationalisms – the Scottish nationalism of the SNP and the Brexit nationalism of the Tory Party.
“If that is the decision before us then everybody loses.”